Question

The length of shadow of a tower on the plane ground is $\sqrt{3}$ times the height of the tower. The angle of elevation of sun is

(a) 45° (b) 30° (c) 60° (d) 90° [CBSE 2012]

Answer 1

Let the angle of elevation of the sun be θ.

Suppose AB is the height of the tower and BC is the length of its shadow.

It is given that, BC = $\sqrt{3}$ AB

In right ∆ABC,

$$\begin{gathered} \tan \theta =\frac{\mathrm{AB}}{\mathrm{BC}} \\ \Rightarrow \tan \theta =\frac{\mathrm{AB}}{\sqrt{3}\mathrm{AB}}=\frac{1}{\sqrt{3}} \\ \Rightarrow \tan \theta =\tan 30° \\ \Rightarrow \theta =30° \end{gathered}$$

Thus, the angle of elevation of the sun is 30º.

Hence, the correct answer is option B.